Method and device for the hysteresis correction of measured values for sensors with extensometers

ABSTRACT

The invention relates to a method and a device for the hysteresis correction of the measured values of one or more sensors ( 1 ), which have been determined in a deformation body using extensometers. According to the invention, each measured value x affected by hysteresis is corrected for the hysteresis error. To achieve this, a hysteresis model is created from the registered strain characteristic curve and the theory of dipole density of the aligned elementary hysteresis in the interior of the deformation body. Said model is used, together with the measured values x affected by hysteresis and the recorded strain history, to derive a correction value for correcting the hysteresis error.

[0001] The invention relates to a method for the hysteresis correctionof measured values in connection with transducers with strain gages,which detect the strain due to a force influence on a deformation body,according to the preamble of the Patent claim 1, as well as an apparatusfor carrying out the method according to the preamble of the Patentclaim 10.

[0002] Measured value transducers with strain gages are often utilizedfor the detection of measured values, whereby the strain gages generatean electrical measuring signal due to a force influence on an elasticdeformation body. In this regard, these transducers are predominantlyutilized in weighing devices for the measuring of forces, moments orpressures. Such transducers and especially weighing cells or load cellsare generally subject to or affected by a hysteresis error, which isrecognizable in practice in that two different measured values areprovided for the same load, depending on whether the measurement iscarried out with a rising or falling load application. The main causefor this ambiguous characteristic curve deviation arefrequency-independent damping processes in the material of thedeformation body in connection with strains in the elastic range, or abeginning plastification in boundary or limit cases. Besides that,external frictional effects also arise on the force introduction orjoint surfaces. Besides other linearity errors, these hysteresis errorsare essentially decisive regarding the accuracy of the measurementresults.

[0003] In practice, these hysteresis errors are often reduced inconnection with weighing or load cells and force transducers in thatthey are compensated to the extent possible by hysteresis effects in theapplication of the converter elements (strain gages). For this purpose,the strain gages and corresponding adhesives are selected, whichcomprise a contrary or counteracting hysteresis to the extent possibleand thereby keep the total hysteresis error small. The hysteresis errorremaining in this manner is, however, subjected to a series scattering,and cannot be removed or corrected even by subsequent processing. Thus,previously, transducers with very small hysteresis errors were producedsimply by selection from the series.

[0004] A method for the reduction of the hysteresis error has similarlybecome known from the DE 20 40 987 B2, wherein this method, in amechanical manner, couples together in a transducer two measuringelements with opposed hystereses. While the hysteresis error can bereduced in this manner, whereby, however, also here, a subsequentprocessing after the fabrication is no longer possible, so that alsohere all tolerances caused by the fabrication go completely into themeasurement result. Moreover, such an apparatus increases the mechanicalstructure enormously due to the production of a complicated and costlymeasurement spring.

[0005] Furthermore, for the correction of the hysteresis error,mathematical methods are also previously known from the GB 147912 B andthe EP 0,457,134 A2, which mathematical methods are utilized in theoutput value of the force transducer. Both publications disclosemathematical methods in the form of polynomial approximations, in which,respectively dependent on the loading direction of the weighing system,stored hysteresis correction values are processed with the determinedmeasured values, and thereafter are output as a weight value correctedby the hysteresis error. Since these methods do not take intoconsideration the local reversal points in the load history, asignificant residual error must remain.

[0006] Therefore, it is the underlying object of the invention, tocorrect a hysteresis error in connection with strain gage transducers,and this at an acceptable expense and effort.

[0007] This object is achieved by the invention recited in the Patentclaim 1 and 10. Further developments and advantageous exampleembodiments are recited in the dependent claims.

[0008] The invention has the advantage that this correction method isutilizable in connection with all hysteresis-affected transducer systemswith strain gages. In this context, it is simply necessary to provide aone-time determination of the loading characteristic curve or individualloading values in rising and falling form, which are sufficient forforming or mapping a hysteresis model, whereupon correction values arederivable for each hysteresis-affected measured value in connection withthe model.

[0009] Furthermore, the invention has the advantage, for the formationof the respective hysteresis model for the special or specifictransducer or the special or specific weighing scale, that only itsloading characteristic curve or only a few determinative loading valuesneed to be determined or prescribed, which already takes place for anormal staggered or graduated measurement for the adjustment, withoutrequiring that the entire loading history must be known, so that noparticular prior determination of a plurality of coefficients isnecessary.

[0010] The invention still additionally has the advantage that thehysteresis correction can be carried out both for one individualtransducer as well as for a plurality of transducers circuit-connectedtogether, for example in a complete weighing scale, since the entirehysteresis error takes place through a downstream or subsequentlycircuit-connected numerical signal preparation or processing. Thereby,it is especially advantageous that this takes place in the simplestmanner due to the derivation of the model from the existence of elasticdipoles, and therefore also requires only a very small computationaleffort or expense.

[0011] In a particular embodiment of the invention it is advantageousthat an adaptation to an unsymmetrical envelope of the hysteresis isalso possible, through an additional weighting function, withoutrequiring that the hysteresis model must have been altered.

[0012] The invention will be described in further detail in connectionwith an example embodiment, which is illustrated in the drawing. It isshown by:

[0013]FIG. 1: a block circuit diagram of the invention;

[0014]FIG. 2: a development of the density function dependent on thestrain history;

[0015]FIG. 3: the envelope of a hysteresis model, and

[0016]FIG. 4: a computer program of the hysteresis model.

[0017] In FIG. 1 of the drawing, the invention is illustrated inconnection with a block circuit diagram, which includes a transducer 1with a pre-amplifier 2, which provides a measured signal x, of which thehysteresis error is corrected by a model circuit 3, a weighting functioncircuit 4, a multiplying circuit 5 and a summing circuit 6.

[0018] The transducer 1 is embodied as a weighing or load cell, whichincludes an elastic deformation body, onto which strain gages areapplied. These emit an electrical signal, that is proportional to theweight loading of the load cell 1. Because this load cell 1 includes adeformation body of an iron alloy, the load cell 1 emits a signal thatis subject to or affected by a hysteresis error, of which the non-linearcourse or progression forms a so-called envelope. Thishysteresis-affected weight signal x is amplified in a followingpre-amplifier 2 and provided to a model computation circuit 3. Loadingvalues are inputted into this model computation circuit 3, wherein theseloading values are run through during a loading of the load cell 1 up toa maximum value and a complete unloading. In this context, beginningfrom an unloaded state, at least one intermediate value is required inthe rising branch, and at least one intermediate value is required inthe falling branch. Such a staggered or graduated measurement withseveral measured values generally is already carried out in theadjustment of the load cell 1 or a weighing scale, so that usually nospecial input of the necessary loading values is required for thispurpose. Moreover, such a loading also does not necessarily have to takeplace in the first use of the load cell 1 or the weighing scale, becauseall previous hysteresis-causing measured values are written over becauseof the measurement up to the maximum value, and therefore can remaindisregarded or not taken into account.

[0019] The hysteresis model of the model circuit 3 is based on theunderlying recognition that the loading history that leads to thehysteresis is developed according to the following steps. For thispurpose, a computational model is utilized, that is derived from thegeometric interpretation of a bending beam. In the manner of a startingpoint, one begins in this context from the existence of elastic dipoles,which orient themselves under the influence of an elastic strain fieldand orient or align themselves in the tension or stress directionsimilarly like the elementary magnets. In the case of the bending beam,the distribution (dipole density φ) is only to be considered over theheight of the spring or of the strain body z. In this context, in afirst approximation, all further spatial components can be neglected.Thereby, also the boundary or edge strain ε_(r) is detectable oracquirable by measurement technology, and the greatest strains arise inthe elastic range on the spring or on the deformation body. Thus, it isassumed for the model, that at this point, a partial aligning ororienting of edge dipoles is forced in the direction of the stressvariations. In this context, the edge or boundary orientation behavesaccording to the following mathematical function:

φ_((Zr)) =C·ε _(r)

[0020] wherein

[0021] φ=dipole density;

[0022] z=spacing distance from the neutral phase in the direction towardthe strain edge or boundary;

[0023] r=characteristic parameter for edge or boundary values;

[0024] ε_(r) =strain at the edge or boundary area; and

[0025] C=factor for hysteresis strength.

[0026] The dipole density φ of the oriented elementary hystereses in theinterior of the body thus arises or is determined from the distortion ordeformation history of the deformation body according to the followingmathematical function

ε_(r)=ΣΔε_(rn)

ε_(rn+1)=ε_(rn)+Δε_(rn+1)

[0027] wherein

[0028] n=number of the load steps.

[0029] For reasons of symmetry, a piecemeal or piece-wise lineardistribution function φ is to be assumed over the height z in a bendingbeam. Therefore, the development of the density function φ can bedeveloped according to FIG. 2 of the drawing with knowledge of theloading history. The course or progression of a first loading andfurther loading cycles is illustrated in FIG. 2 of the drawing. Onebegins with φ=constant=0.0 and ε_(r)=0.0. The boundary or edge strain isincreased to ε_(r)=A. Thereby, the density function becomes adjustinglyset to the course or progression A-B. If next the initial conditionε_(r)=0.0 is again forced, then the point C arises, and the orientedregion 0-C-B remains behind in the interior. If the boundary or edgestrain is again increased, thereby the front A′-C′ is formed parallel toA-B. Upon reaching ε₁, point C′ transitions into C, whereby acancellation of both points takes place. A sign reversal in the strainvelocity causes a new instability or discontinuity point in φ at thebody edge. This point can move or wander only in the direction towardthe neutral fiber (NF). Fronts between two instability or discontinuitypoints are immovable, only the line segment between the edge and thefirst point is shifted in a parallel manner. Points that run togetheragain mutually cancel each other. With a sufficiently large boundary oredge strain, independent of the sign, every older internal structure isoverwritten by the new front B′. If thereby two instability ordiscontinuity points cancel each other out, there thus arises a kink orbend in the characteristic curve branch. In a weakly damped decayingoscillation, beginning with the maximum amplitude in ε_(r), the entirestored information is cancelled or erased.

[0030] The failure or fault moment of a single individual fiber is to beobtained from the geometric conception, through the density function φthat is multiplied with the fiber spacing z. An internal hysteresismoment M_(h) or an internal hysteresis force F_(h), which is held inequilibrium balance by a boundary or edge strain error ε_(h), isobtainable from the integration over z and a multiplication with thefactor C (hysteresis strength). This remaining hysteresis moment M_(h)or hysteresis force F_(h) arising out of the loading history, arises oris given according to the following mathematical function:M_(h) = C_(m) ⋅ ∫_(−zr)^(+zr)ϕ(z) ⋅ z⋅  z  or  F_(h) = C_(f) ⋅ ∫_(−zr)^(+zr)ϕ(z) ⋅ z⋅  z

[0031] In this context, the factor C is first selected so that therelative model hysteresis becomes 100%. The adaptation to the transducerhysteresis that is to be corrected can then additionally be carried outthrough a weighting function P_((x)) in a weighting circuit 4. From thethusly developed model, which essentially contains or includes theloading history, a correction or auxiliary value h is calculable foreach determined measured value x. In this context, the hysteresis modelessentially describes the linearity deviation from a straight line inthe teardrop shape of the envelope loop. Such an envelope of theauxiliary value h over the hysteresis-affected measured value x is shownin FIG. 3 of the drawing. Thereby, this envelope 7 represents orillustrates a symmetrical teardrop shaped course or progression, ofwhich the values are respectively calculated in the model circuit 3according to the program in FIG. 4. In this context, the hysteresismodel is described in the programming language “FORTRAN” and is inputinto the model computation circuit 3, which therewith calculates therespective auxiliary value h for each measured value x. Since theenvelope 7 according to the model circuit 3 describes an envelope inideal teardrop shape according to FIG. 3 of the drawing, an adaptationto unsymmetrical hysteresis curves, which deviate from this teardropshape 7, can still be carried out. For this purpose, a weightingfunction is still provided, which describes a linear dependence P_((x))through which the unsymmetries of the hysteresis curves can additionallybe taken into account in the weighting circuit 4. Since an adaptingfactor C of the transducer hysteresis is still further contained in thisweighting function P_((x)), the model computation circuit 3 can be usedfor all hysteresis-affected transducers.

[0032] In a following multiplying circuit 5, the weighting functionP_((x)) as the form of the respective weighting factor w ismultiplicatively coupled with the respective auxiliary value h andprovided to a summing circuit 6 as a correction factor. This weightingfactor w can, in the ideal case for an ideal teardrop shape 7 of theenvelope, possess the factor 1 as described above, or can contain anadaptation of the measured hysteresis to the relative model hysteresis.Since also a linear adaptation to a deviation of the ideal teardropshape 7 of the hysteresis model can be contained by this weightingfunction, the weighting function circuit 4 still additionally calculatesthe respective deviation relative to the determined hysteresis-affectedmeasured value x. The total weighting factor w resulting herefrom,multiplied with the auxiliary value h gives, at the output of themultiplier 5, a correction value for taking into account the respectivehysteresis error.

[0033] In the summer 5, the determined correction value is additivelycoupled with the correct sign with the hysteresis-affected measuredvalue x, so that thereafter the measured value y that has been cleanedwith respect to the hysteresis error is then available for furtherprocessing or for indication at the output of the summer 6.

[0034] Such a correction method can be carried out as well by means ofhardware or software-based computational circuits. In this context, sucha correction method is suitable both for analog as well as for digitaltransducer circuits or weighing scales.

[0035] Particularly, it requires no special adaptation to the specialembodiment of the transducers or weighing scales, but rather it cansimply be carried out by receiving or taking up the falling and risingloading characteristic curves.

1. Method for the hysteresis correction of measured values in connectionwith transducers with strain gages, which detect the strain due to aforce influence on an elastic deformation body, in which thehysteresis-affected measured values are corrected by a determinedhysteresis error, characterized in that a hysteresis model is formedfrom determined loading values in a rising and a falling loading branch,with the aid of which, and from each determined hysteresis-affectedmeasured value x, a correction value is derivable or calculable, whichserves for the correction of the hysteresis error.
 2. Method accordingto claim 1, characterized in that a hysteresis model of the transducer(1) is formed in a model circuit (3) from the dipole density φ of theoriented elementary dipoles in the interior of the deformation body andthe determined loading values in the rising and falling loading branch(envelope (7) of the hysteresis).
 3. Method according to claim 1 or 2,characterized in that an auxiliary value h is formed from the formedhysteresis model and respectively from a hysteresis-affected measuredvalue x in the model circuit (3), which auxiliary value h represents avalue for the relative hysteresis error.
 4. Method according to claim 3,characterized in that a weighting factor w is formed from the determinedloading values (envelope (7) of the hysteresis) of the transducer (1) ina weighting circuit (4) by means of a weighting function P.
 5. Methodaccording to claim 3, characterized in that a weighting factor w isformed from the determined loading values (envelope of the hysteresis)of the transducer (1) and/or from an unsymmetry of the envelope (7) bymeans of s a weighting function P_((x)).
 6. Method according to claim 4or 5, characterized in that a weighting factor w is formed from theweighting function P_((x)) and from a respectively determinedhysteresis-affected measured value x in the weighting circuit (4), andthis weighting factor is multiplicatively coupled with the auxiliaryvalue h and gives a value for the respective hysteresis error.
 7. Methodaccording to claim 6, characterized in that the value of the respectivehysteresis error is coupled with the hysteresis-affected measured valuex with a correct sign in a summing circuit (6), and gives a measuredvalue y that is corrected by the hysteresis error.
 8. Method accordingto one of the preceding claims, characterized in that thehysteresis-affected measured value x is determined as the output signalof a transducer (1) or as the output signal of several transducers (1)that are circuit-connected together.
 9. Method according to one of thepreceding claims, characterized in that the output signals x are formedas well from sampled analog signals or as digital values.
 10. Apparatusfor carrying out the method according to one of the preceding claims,characterized in that a transducer (1) with strain gages is provided, ofwhich the hysteresis-affected measured values x are delivered to a 5model circuit (3), which therefrom forms an auxiliary value h, which iscoupled in a provided multiplication circuit (5) with the weightingfactor w formed from a provided weighting circuit (4) to form acorrection value, and from which, in a provided summing circuit (6),under consideration of the hysteresis-affected measured value x, at theoutput of which the corrected measured value y is available for furtherprocessing or indication.
 11. Apparatus according to claim 10,characterized in that the model circuit (3), the multiplying circuit(5), the weighting circuit (4) and the summing circuit (6) is embodiedin a hardware manner as an electronic circuit.
 12. Apparatus accordingto claim 10, characterized in that the functions of the model circuit(3), the multiplying circuit (5), the weighting circuit (4) and/or thesumming circuit (6) is embodied as a program-controlled electroniccomputer circuit.